Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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            <s xml:id="echoid-s9729" xml:space="preserve">AD eaſdem partes vergentium curvarum, è communi quadam
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            generatione deductas, generales aliquot affectiones jam antea
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            dudum expoſui; </s>
            <s xml:id="echoid-s9730" xml:space="preserve">illas præſertim, quas à veteribus _Geometris_ obſer-
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            varam ſpecialibus, quas ipſi tractant, curvis applicari. </s>
            <s xml:id="echoid-s9731" xml:space="preserve">Jam non
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            ingratum facturus videor, ſi complures alias (abſtruſiores quidem
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            illas, at non injucundas prorſus, aut inutiles) appoſuero; </s>
            <s xml:id="echoid-s9732" xml:space="preserve">pro mèo
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            more quàm conciciſſimè demonſtratas, eâ tamen ratione quoad po-
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            tero, quæ cumprimis ſcientifica videtur, hoc eſt quæ nedum con-
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            cluſionum veritatem aſſerit, at fontes etiam aperit, unde illa pro-
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            manat. </s>
            <s xml:id="echoid-s9733" xml:space="preserve">Verſantur autem præcipuè quæ proferemus, partim _circa_
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            _tangentium abſque calculi moleſtia vel faſtidio inveſtigationem ſi-_
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            _mul ac demonſtrationem expeditam_ (è ſimplicioribus nempe vulga-
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            tioribúſque perplexiora minúsque perſpecta deducendo) _partim cir-_
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            _ca mnltarum magnitudinum dimenſiones, tangentium deſignatarum o-_
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            _pe, quam promptiſſimè determinandas_; </s>
            <s xml:id="echoid-s9734" xml:space="preserve">quæ materiæ cùm præ Ge-
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            ometricis aliis quodammodò difficiles videntur, tum non penitus
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            adhuc (ſicut aliæ quædam) occupatæ vel exhauſtæ ſunt, ad hunc
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            ſaltem modum quod ſciam nondum tractatæ Quin è veſtigiorem aggre-
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            dimur, _Lemmatica_ quædam utcunque, quorum in reliquis clariùs & </s>
            <s xml:id="echoid-s9735" xml:space="preserve">
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            breviùs oſtendendis aliquem proſpicimus uſum, prælibantes.</s>
            <s xml:id="echoid-s9736" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s9737" xml:space="preserve">II Sit _angulus rectilineus_ ABC, & </s>
            <s xml:id="echoid-s9738" xml:space="preserve">datum punctum D, ſit i-
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              <note position="right" xlink:label="note-0223-01" xlink:href="note-0223-01a" xml:space="preserve">Fig. 38.</note>
            tem linea ODO talis, ut per D ductâ quâvis rectâ DN; </s>
            <s xml:id="echoid-s9739" xml:space="preserve">ſit an-
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            guli lateribus intercepta MN æqualis à puncto D, & </s>
            <s xml:id="echoid-s9740" xml:space="preserve">linea ODO
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            interceptæ DO; </s>
            <s xml:id="echoid-s9741" xml:space="preserve">erit linea ODO _Hyperbola._</s>
            <s xml:id="echoid-s9742" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s9743" xml:space="preserve">Nam ducatur DL ad CB parallela occurrénſq; </s>
            <s xml:id="echoid-s9744" xml:space="preserve">ipſi AB in L; </s>
            <s xml:id="echoid-s9745" xml:space="preserve">& </s>
            <s xml:id="echoid-s9746" xml:space="preserve">
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            in protracta BL ſumatur LZ = LB; </s>
            <s xml:id="echoid-s9747" xml:space="preserve">ducatúrq; </s>
            <s xml:id="echoid-s9748" xml:space="preserve">ZS ad BC paral-
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            lela; </s>
            <s xml:id="echoid-s9749" xml:space="preserve">item ducatur OK ad BZ parallela. </s>
            <s xml:id="echoid-s9750" xml:space="preserve">Et ob poſitam DO = MN;
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            </s>
            <s xml:id="echoid-s9751" xml:space="preserve">erit HO = BN; </s>
            <s xml:id="echoid-s9752" xml:space="preserve">ergò quum ſit DH. </s>
            <s xml:id="echoid-s9753" xml:space="preserve">HO:</s>
            <s xml:id="echoid-s9754" xml:space="preserve">: (DL. </s>
            <s xml:id="echoid-s9755" xml:space="preserve">LN:</s>
            <s xml:id="echoid-s9756" xml:space="preserve">: </s>
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